A205424 Number of (n+1) X 2 0..3 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..3 introduced in row major order.

15, 102, 870, 7566, 68342, 609086, 5514982, 49362414, 446198614, 4001326366, 36118081094, 324279012558, 2924285830070, 26275991783678, 236797822738342, 2128866218464686, 19176856665755158, 172465933376949982

Offset

1,1

Comments

Column 1 of A205431.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) + 73*a(n-2) + 39*a(n-3) - 384*a(n-4) - 432*a(n-5) for n>6.

Empirical g.f.: x*(15 + 87*x - 327*x^2 - 1335*x^3 - 952*x^4 + 144*x^5) / ((1 - 9*x)*(1 - x - 4*x^2)*(1 + 9*x + 12*x^2)). - Colin Barker, Mar 03 2018

Example

Some solutions for n=4:
  0 0   0 0   0 0   0 1   0 0   0 0   0 0   0 0   0 1   0 1
  0 0   0 1   0 0   0 1   0 0   0 0   0 0   0 0   1 0   0 1
  0 1   2 1   0 1   0 0   1 1   0 1   0 1   0 1   2 1   0 0
  0 1   0 2   1 0   1 1   1 1   2 1   2 3   1 0   1 2   0 0
  1 2   3 1   1 0   2 1   2 1   1 0   3 0   2 0   0 3   1 1

Crossrefs

Cf. A205431.

Sequence in context: A093739 A205431 A085465 * A219624 A219170 A227331

Adjacent sequences: A205421 A205422 A205423 * A205425 A205426 A205427

Keyword

nonn

Author

R. H. Hardin, Jan 27 2012

Status

approved